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Exercise 8.25

Exercise 8.25. Stat 121 KJ Wang. Votes for Bush and Buchanan in all Florida Counties. Palm Beach County (outlier). Log Transformation. Data excluding Palm Beach County. S Plus Model for data w/o Palm Beach County. *** Linear Model ***

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Exercise 8.25

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  1. Exercise 8.25 Stat 121 KJ Wang

  2. Votes for Bush and Buchanan in all Florida Counties Palm Beach County (outlier)

  3. Log Transformation

  4. Data excluding Palm Beach County

  5. S Plus Model for data w/o Palm Beach County • *** Linear Model *** • Call: lm(formula = buchanan2000 ~ bush2000, data = ex0825, na.action = na.exclude) • Residuals: • Min 1Q Median 3Q Max • -512.4 -47.97 -17.09 41.78 305.5 • Coefficients: • Value Std. Error t value Pr(>|t|) • (Intercept) 65.5735 17.3304 3.7837 0.0003 • bush2000 0.0035 0.0003 13.9226 0.0000 • Residual standard error: 112.5 on 64 degrees of freedom • Multiple R-Squared: 0.7518 • F-statistic: 193.8 on 1 and 64 degrees of freedom, the p-value is 0

  6. CI Attempt 1 • Formula: Buchanan Votes = (0.0035)Bush Votes + 66 • 95% CI = fitted +/- t*SE(fitted) • Intercept = 66 +/- 17.3*(1.99773) = 100.5, 31.5 • Coefficient = 0.0035 +/- 0.0003(1.99773) = 0.0041, 0.0029 • Bush = 152846 • Predicted High with 95% CI: 152846 *0.0041 + 100.5 = 727 • Predicted Low with 95% CI: 152846 * 0.0029 + 31.5 = 475 • THEREFORE: Predicted number of votes Buchanan should have received in Palm Beach County based on the number of votes Bush received is 475-727 • Buchanan actually received 3407 votes in Palm Beach County • IF the statistically extra Buchanan votes were intended for Gore, then Gore should have received at least (3407-727 =) 2680 more votes.

  7. CI Attempt 2 • Formula: Buchanan Votes = (0.0035)Bush Votes + 66 • 95% CI = fitted +/- t*SE(predicted) • SE(predicted) = square root(σ^2 + SE(fit)^2) • σ = Residual Standard Error = 112.5 • SE(fit) = 31.05 • Buchanan(predicted) =597.77 • SE(pred) = root(112.5^2 + 31.05^2) = 116.7058 • qt(.975, 64) = 1.99773; qt(.975,64)*SE(pred) = 233.0965 • Buchanan(predict) = 597.77 +/- 233.0965 • THEREFORE: Predicted number of votes Buchanan should have received in Palm Beach County based on the number of votes Bush received is 365 - 831 • Buchanan actually received 3407 votes in Palm Beach County • IF the statistically extra Buchanan votes were intended for Gore, then Gore should have received at least (3407-831 =) 2576 more votes.

  8. FINAL CONCLUSION • Gore would have won the election if the voters in Palm Beach followed the same statistical model as the rest of the state • 2576 extra votes is more than Bush’s initial margin of victory of 1738 votes • BUT TOO BAD!

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